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We give an informal summary of ongoing work which uses tools distilled fromthe theory of fibre bundles to classify and connect invariant fields associatedwith spin motion in storage rings. We mention four major theorems. One tiesinvariant fields with the notion of normal form, the second allows comparisonof different invariant fields and the two others tie the existence of invariantfields to the existence of certain invariant sets. We explain how the theoremsapply to the spin dynamics of spin-$1/2$ and spin-$1$ particles. Our approachelegantly unifies the spin-vector dynamics from the T-BMT equation with thespin-tensor dynamics and other dynamics and suggests an avenue for addressingthe question of the existence of the invariant spin field.

An Informal Summary of a New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles